383 Runs Rough, Will not stay cranked

I have a 68 Dodge Monaco. It was my dad's car I got in 2005 when he died. He was a very good shadetree mechancic and rebuilt the engine in 1995, drove it a little, and then let it set for years. I got the car and restored it - new paint job, repaired gas tank, etc., everything needed to get it running again. It's ran good for 7 years now. I had driven the car in February and it ran as usual, no problems. Next time I tried to drive was in June - I know, I shouldn't let it set that long and that's the first time that's happened. In June, when I cranked, it ran rough, missing, wouldn't idle. Finally died after ~10-12 seconds and wouldn't crank at all after that. Note - when it's set for a while, I always just poured a little gas in the carb, and it would fire right up and run okay after a few seconds. But this time, it was a very rough idle, missing, died. So I'm thinking ignition. It still had the points/condenser setup, so I finally broke down and replaced this weekend with the electronic ignition module and new coil. Poured a little gas in the carb, and it cranked, but same thing - running like crap. I could keep it running, even though rough, but I was by myself and couldn't get to the front and keep it going to check anything. So when I let off the gas, it died. Never could get it to crank again. I know the problem is not in the firing order because absolutely nothing had been done since it ran okay in February. I did not replace the distributor cap because again, it was okay in February. So not sure of the problem. Maybe fuel issue? I did change a fuel filter I had put in right before the fuel pump. It looked bad - sort of gummed up. That didn't help, still wouldn't start. I started thinking old gas, but that doesn't make sense because I'm pouring new/good gas in carb to start - it should at least fire. Voltage regular? Could carb be gummed up causing this? Carb is new 4-barrel Edelbrock installed in 2006. I'm not sure where to go right now with it and asking for help/suggestions. Thanks

Could be fouled plugs but wouldn't even a fouled plug(s) still fire somewhat after the car ran bad after initially cranking. There was no fire at all after the initial crank - both June and past Sunday. You would think it would at least try and crank again, and run bad again. Wouldn't even do that.

I did jumper across the ballast resistor with a wire. I didn't remove the resistor, just put a wire between the plugs - I think that should do it.

Electronic ignition I installed was an Accel POINTS ELIMINATOR CONVERSION PART NO. 2030. The coil was an Accel 8140 Cannister coil. Instructions say can use without ballast resistor if using this coil - that's why jumpered across the plugs.

Some more info - talking with a friend who has always messed with older cars. Subject of battery came up. Both times car cranked and ran bad, I had just charged battery. Both times car cranked on first try. Subsequent to first crank after going dead, you could easily hear battery going down fast trying to re-crank. You couldn't crank the car more than 10-12 seconds or so without getting close to zero. I would put the charger back on the battery while I was checking other things and re-cranking. Battery never did go back to full after first crank. Can the battery have insufficient voltage to maintain good spark/fire, but have to enough to engage starter? Battery is 7 years old. To eliminate this altogether, I went out last night a bought a new battery from Advance Auto - they had a coupon for $40 off purchase over $100. So the car gets a new battery and eliminates low voltage/bad battery as a potential problem, even if it wasn't one.

My friend also mentioned a test light, which you advise as well. I'm going to swing by parts place and get one next day or so.

this is a coil output tester .. available at most parts stores for under 8 bucks..

you can even make your own...

or just position the end of the coil wire 1/2" away from the engine block..

please.. DON'T hold the coil wire with your hand.. while this is being done..

it may turn into a shocking experience..

it takes a minimum of diagnostic tools to work on cars...

a digital volt meter.. since you don't have points.. you can get by with a conventional volt meter as is shown above..

a test light..

a spark tester...

a timing light, a vacuum gauge, are also part of a minimum diagnostic tool kit..

a remote starter button also helps a LOT...

i expect that you have a spark plug socket and enough hand tools to change them.. and on mopars that can be a challenge.. i used to do the spark plugs on my aunts 68 new yorker.. from under the car.. it was quicker.. but that was a 440..